Bouye, a Pro Bowler in 2017, will be suspended for the first two games of the 2021 season as part of a six-game ban he received last year for violations of the league's policy on performance-enhancing substances.
He will be allowed to participate in offseason and preseason practices, according to the league.
Carolina signed 10-year veteran corner Rashaan Melvin to a one-year deal earlier in free agency.
Bouye, 29, was released by Denver in February after appearing in only seven games because of injuries and the suspension. He was traded to the Broncos from Jacksonville in March 2020, after being a big part of the Jaguars' run to the AFC Championship Game in the 2017 season.
Bouye entered the NFL in 2013 with Houston as an undrafted free agent. He played well enough that he received a five-year, $67.5 million deal with Jacksonville in 2017.
He had six interceptions that season in 16 starts. He has only two picks since, and he had none for Denver last year. In 69 career starts, he has 14 interceptions overall.
Bouye likely will be penciled in as the starter in Carolina opposite Donte Jackson, who is in the last year of his rookie deal.
The former Central Florida standout will compete with Melvin, likely on the right side.
The addition of Bouye lessens the urgency to use the No. 8 pick of the draft on a corner. The team eliminated the necessity to draft a quarterback on Monday after trading with the New York Jets for Sam Darnold, but general manager Scott Fitterer said that doesn't totally precluded using the eighth pick on that position.
"What we wanted to do going into this draft through free agency, through this trade with Sam, was to just get rid of all the needs we have,'' Fitterer said Monday. "We wanted to get to a place where the roster was in a good spot, and we could take the best player at No. 8.''